Total ion flux in a Polywell - disruption to magnetic field?

[chrismb]

Hi.

I thought I'd pop in to talk-polywell.org forum, off from the fusor.net site, to see if I can discuss a few issues of [im-]practicality I am curious over.

Consider the proton-boron collision at 550keV = 1.2barns.

And the closing velocity is 12/11*a proton at 550keV = ~11Mm/s.

Let's say that the peak boron particle density that the proton passes through is 1E19/m3 (equivalent to 1 micron).

The mean path to a fusion event for a proton is therefore 1/(1E19/m3).(1.2E-28m2) = 900 million metres.

To generate 1watt of fusion power from p11B (8.68MeV) we need 720 billion reactions per second.

Now let's say that one reciprocation of these particles is a 1 m path length. So we'll need 900 million particles doing this loop to get one reaction in one loop. We also need 720 billion times this number, per second, to hit our 1W target.. That's a total of 6.48E20 protons per second. That's 100 amps worth of protons passing through this ball of 'confined electrons' – all for 1 W of fusion output.

So if you get to, say, a mere 10kW of fusion power output, the peak consumption I need for my house, won't this 1MegaAmpere proton flux tend to disrupt the magnetic fields holding this ball of electrons together??

(I've been on the generous side here with collision energy/cross-section, particle density and an assumption of zero scattering.)

I can anticipate there may be an argument put forward that magnetic fields induced by these huge proton fluxes may be symmetrical (though the electrons aren't), but just as you can't generate a uniform spherical magnetic field, so you can't expect the resultant net field to be uniform either, so the fields will twist and tumble as the ions pass through the centre.

That should be good enough to generate several tesla of field disruption in the central electron confinement.

Am I missing/misunderstanding something here?

best regards,

Chris MB.

[TallDave]

Let's say that the peak boron particle density that the proton passes through is 1E19/m3 (equivalent to 1 micron).

Curious where this # comes from. The only density numbers I've seen are from when Rick Nebel did a comparison to ITER where he found an equivalent Polywell would be around 2.5e22/m^-3 at the edge, and maybe a few orders of magnitude better towards the center.

[TallDave]

Ah, here we go:

http://www.askmar.com/Fusion_files/Poly ... oncept.pdf

Table 1 anticipates core density of 2e24/m^-3 in a fusion reactor. But this paper is from 1992 (albeit updated with pics in 2007), so if anyone has something more recent please share.

[chrismb]

Ah, here we go:

http://www.askmar.com/Fusion_files/Poly ... oncept.pdf

Table 1 anticipates core density of 2e24/m^-3 in a fusion reactor. But this paper is from 1992 (albeit updated with pics in 2007), so if anyone has something more recent please share.

Where did I get 1E19 from? - an inspired guess! not bad, considering the 'experimental' reactor is quoted at 4E19?

OK, let's go with the 'fusion reactor' data which is predicting a core plasma of 1/10th of atmospheric density:

1/(2E24/m3).(1.2E-28m2) = 4100 metres.

[I am somewhat uncertain about the ability of a man-made fusion device to reach near to atmospheric pressure simply by the attraction of electrons. Is there experimental evidence to show this is possible?]

Core diameter = 2E-2. So number of reciprocations to pass through 4100meters worth of core = 205000

To generate 800Megawatts of fusion power from p11B (8.68MeV) we need 5.7E20 reactions/s.

So we'd need 205000 reciprocations 5.7E20 times per second = 1.2E26 protons per second = ~20MegaAmperes flux

(and that's just the protons)

That 20MA of proton flux has to be fully drawn into the central core without any emittance permitted.

What is the acceptable emittance of particles heading towards the centre, and what is the total population (charge) of the central core of electrons required to achieve this maximum emittance?

[MSimon]

Chris,

IIRC huge circulating currents were predicted for Polywell. I'd have to look up the number but I believe they were in the range you estimated.

[chrismb]

Chris,

IIRC huge circulating currents were predicted for Polywell. I'd have to look up the number but I believe they were in the range you estimated.

So, at what ion flux does magnetic field disruption occur? There must be some rate at which this happens such that it becomes significant in comparison to the confining fields.

It would be one thing to show a very small ion flux is viable, but quite another to show these megaamp ion fluxes are sustainable. I presume there will be some cut-off point (when internally-generated fields become comparable with imposed fields) which would not be something that can be extrapolated to.

best regards,

Chris MB.

[MSimon]

Chris,

IIRC huge circulating currents were predicted for Polywell. I'd have to look up the number but I believe they were in the range you estimated.

So, at what ion flux does magnetic field disruption occur? There must be some rate at which this happens such that it becomes significant in comparison to the confining fields.

It would be one thing to show a very small ion flux is viable, but quite another to show these megaamp ion fluxes are sustainable. I presume there will be some cut-off point (when internally-generated fields become comparable with imposed fields) which would not be something that can be extrapolated to.

best regards,

Chris MB.

More experiments are required at longer time frames - seconds to minutes. Pulse experiments are not going to cut it for definitive answers.

BTW the ion fluxes will be countered to some extent by electron fluxes. If they counter rotate they should mostly cancel. Or if the ions drag electrons (or vice versa).

[Art Carlson]

Any place you have ions going north, you have just as many ions going just as fast south. There is practically no *net* ion current. (Ditto for electrons).

[MSimon]

Any place you have ions going north, you have just as many ions going just as fast south. There is practically no *net* ion current. (Ditto for electrons).

Art,

Myself being a mere engineer could you explain why that is so?

[Art Carlson]

Any place you have ions going north, you have just as many ions going just as fast south. There is practically no *net* ion current. (Ditto for electrons).

Myself being a mere engineer could you explain why that is so?

It doesn't *have* to be that way. It's just that a polywell is designed that way. In the usual picture, an ion is let loose at the top of the well, it zooms through the middle and up the other side of the well. It slows down and turns around and then zooms through the middle again, but this time coming from the other direction. Good idea, too. If all the ions were going the same way, you wouldn't have any collisions to give you fusion.

[MSimon]

OK. I see your point.

However if you get bunching and oscillations it might not actually work that way.

Although simulations suggest that even with bunching the beams will co-ordinate and all go out and come in synchronously so the net current will be low although local currents might be rather high.

There really is so much we do not know.

[chrismb]

OK. I see your point.

However if you get bunching and oscillations it might not actually work that way.

Yes. That's the point I am trying to get to. As all this huge flux of ions run into the centre, they're not all going to be coming in perfectly symmetrical.

Is the ball of electrons perfectly symmetrical? I understand it has various cusps, so clearly not.

As a variably distributed stream of charge enters the central region, surely it can't all bunch up smoothly into some small area? It's going to bunch and pull and rotate around chaotically as all the ions push to get to the centre.

A bit like the models for the interior of the earth's magnetic field. ( http://graphics8.nytimes.com/images/200 ... T_span.jpg )

Magnetic fields are generated between charged particles moving in different directions and at different velocities. Magnetic fields are not generated by particles on parallel tracks, they are generated, for example, between particles that are converging on a point, subtending an angle. This is exactly the case for Polywell's intent.

[drmike]

The ion currents are mostly radial, so the net current is pretty much zero. Near the MaGrid
the velocity is zero, and near the center the sum of all velocities is zero, so the current is
zero at those points. In between there may be a few oscillations, but the net current flow
is pretty small. At least for a stable system it should be.

Even in the cusps you still get radial symmetry - things just go out a little farther along those
lines. Some things won't stop! But that's a small loss (hopefully), and also won't add up to
much current.

This is one of the reasons I don't think an octa-coil will work. It's not spherically symmetric.
But it will be interesting to test that!

[chrismb]

The ion currents are mostly radial,

Is that a statement of fact, experimental measure, guess-work, or other?

Is there any supporting evidence to this claim, or does it represent an intuitive assumption?

If you had never actually seen water go down a plug hole, you might think it would go 'straight-down' radially, as well.

Notwithstanding scales of effects and other endless caveats, what is the fundamental conceptual difference between water going down a plug hole and ions heading into the central core?

If all of this has proper answers, I would still pick up on your own word 'mostly'. Instabilities fundamentally occur when small disturbances seed a greater disruption. To counter that argument, there would have to be a clear mechanism within the dynamics of a system that naturally damps the processes of disruption. In the case of radial ions, I would surmise that non-radial motion of the ions must cause local magnetic disruption to both ions and electrons, which then would feed back into that disruption, so I see no system damping going on.

Blind faith might have you believe such disruptions won't spoil your party, but a realistic historical examination of any physical investigation into dynamical systems will tell you something else, e.g. tokamak.

[Art Carlson]

I agree with Chris that an ion velocity distribution with purely radial velocities will be highly unstable. I assume that the distribution will be everywhere nearly isotropic, and not too far from Maxwellian. That contradicts the polywell orthodoxy, but even Rick Nebel doesn't seem to insist very strongly on this point.